Any thinking person is likely to spend at least a portion of his too-brief time on earth trying to solve the riddle of existence. Even the most devout believers can find themselves struggling with the seemingly unfathomable workings of God.

Now comes Rajiv Joseph’s “Bengal Tiger at the Baghdad Zoo,’’ which raises the cheerless prospect that these questions will persist even after death.

It is a mark of Joseph’s original turn of mind that this bleak and unsettling vision is chiefly embodied by the curmudgeonly tiger of the title.

In the New England premiere of “Bengal Tiger’’ at Company One, directed by Shawn LaCount, the tiger is portrayed by the burly, bearded, and barefoot Rick Park, glowering and fuming as he stalks the stage in a ragged gray coat, white shirt, and orange scarf.

After he is shot dead at the zoo by a US Marine in the aftermath of the 2003 invasion of Iraq, the tiger proceeds to haunt the American, even as he is himself haunted by matters of guilt, sin, redemption, freedom, cruelty, suffering, and individual purpose. “See, all my life, I’ve been plagued, as most tigers are, by this existential quandary: Why am I here?” he says. “But now . . . I’m dead, I’m a ghost . . . and it’s: Why aren’t I gone?’’ He adds: “When an atheist suddenly finds himself walking around after death, he has got some serious reevaluating to do.’’

Nobody’s really gone in “Bengal Tiger.’’ Eventually, the stage of the Plaza Theatre is more populated by the dead than by the living. Two Marines, Kev (Michael Knowlton) and Tom (Raymond Ramirez), as well as an Iraqi translator named Musa (Michael Dwan Singh), are forced to do some serious reevaluating of their own lives and their own choices.

It’s a uniformly strong cast, and LaCount, the artistic director of Company One, is attuned to the play’s complexity. He brings to “Bengal Tiger’’ the clarity and force he achieved a couple of months ago at the helm of Kristoffer Diaz’s “The Elaborate Entrance of Chad Deity.’’ The faded grandeur of Dahlia Al-Habieli’s set evokes Iraq’s deep history, while sound designer Edward Young effectively conveys the havoc of a city under siege.

That winking line above — “plagued, as most tigers are’’ — is not the only instance of sly humor in “Bengal Tiger,’’ which was a finalist for a 2010 Pulitzer Prize and ran on Broadway last year, starring Robin Williams. Much of Joseph’s grim wit is channeled through the tiger. Park, excellent throughout, is especially amusing when the tiger fumes about the foolhardiness of “the Leos,’’ eight lions who escaped from captivity when the zoo wall was blown up and raced into the streets of Baghdad, exulting in their freedom, only to be pulverized by artillery.

That’s the world of “Bengal Tiger’’ in a nutshell. Blindly impulsive actions — like, say, invading a sovereign nation on spurious grounds — have large and enduring consequences. The playwright’s concerns are ultimately more philosophical than political: In conjuring the chaotic, unpredictable, no-rules atmosphere of wartime, Joseph suggests that a similar randomness governs the universe.

The concerns of the two Marines are, at first, strictly with the spoils of war. Arousing Kev’s deep envy, Tom has in his possession a gold-plated semi-automatic pistol that belonged to Uday Hussein, the notoriously brutal son of Saddam Hussein, obtained during the raid by US troops that killed Uday. Tom also has Uday’s gold toilet seat, won in a poker game. But the Marine’s luck runs out big-time when he taunts the tiger, who promptly bites his hand off, whereupon Kev shoots the tiger with the gold gun. The three of them were thrown together by chance, but their paths will cross again.

As for Musa, the translator, he is treated contemptuously by the Marines, as a mere means to an end. His anger at the treatment of his countrymen steadily builds. But the anguish of Musa, who had been a gardener for Uday Hussein, is rooted in a specific and horrific prewar event, an important reminder by the playwright that it is always average citizens like Musa who are caught in the middle of power struggles.

As Uday, attired in a lounge-lizard burgundy suit (the costumes are by Lara de Bruijn), Mason Sand creates an indelible portrait in evil. An unquiet afterlife is just fine with Uday. “Americans!’’ he sneers. “Always thinking that when things die, they go away.’’